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  • The determinant is the scalar value resulting from certain operations on the elements of a square matrix (a matrix with the same number of rows and columns). The determinant provides important information about the properties of the matrix, such as whether or not the matrix has an inverse. If the determinant of a matrix is not equal to zero, then the matrix has an inverse. Determinants are also used in a variety of applications, including the calculation of area, volume, and coordinate transformations in math and physics.

    A matrix inverse is a matrix that, when multiplied by the original matrix, produces the identity matrix. The identity matrix is a square matrix that has elements of 1 along the main diagonal and 0 in the other elements. Only square matrices that have a determinant not equal to zero have an inverse.